Such a measurement apparatus is known from DE 20 2011 105 077 U1. There, the feed movement of a workpiece by a belt arrangement with a belt that is conducted over deflection rollers and pressed against the workpiece is detected. To this end, the belt is pressed by the pressure elements that are also moved with it, for example, against the underside of a workpiece that is moved on a workpiece support in the longitudinal direction. By means of the pressure elements moved along with the belt, the belt can be pressed against the workpiece to attain a slip-free connection with the workpiece, without a sliding friction appearing between the pressure element and the belt. On at least one of the deflection disks of the belt, a sensor or another suitable device for the detection of its rotating movement can be located. By detecting the rotating movement of the deflection disk that is driven by the workpiece via the belt, it is thus possible to detect the movement of the workpiece and to measure it slip-free. However, the belt arrangement in this known measurement apparatus has only limited movement possibilities, which, in particular with irregularly shaped workpieces, can lead to measurement inaccuracies.